Finding roots with C

#include <stdio.h>
#include <math.h>
#define PI 3.14159265

double f(double x);
double direct(double a, double b, int n);

int main()
{
		double  x0 = 12.0, xn = 16.0;
		int n = 400;

		printf( "The root is %f\n", direct(x0, xn, n) );

		return 0;
}

double f(double x)
{
		double y;

		y = 667.38/x * (1 - exp(-0.146843*x)) - 40.0;
		return y;
}
double direct(double a, double b, int n)
{
		int i;
		double dx, x, f1, f2;

		dx = (b - a) / n;
		f1 = f(a);
		for (i = 1; i <= n; i++) {
			x = a + dx * i;
			f2 = f(x);
			if (f1 * f2 <= 0) break;
			f1 = f2;
		}
		return x - dx/2;
}

Here is my Newton-Raphson method code.

#include <stdio.h>
#include <math.h>
#define EPS0 1.0e-12
double f(double x);
double fp(double x);
double newton_raphson(double x, double eps);

int main()
{
		double  xi = 0, eps = 1.0e-6;
		printf( "The root is %f\n", newton_raphson(xi, eps) );
		return 0;
}

double f(double x)
{
		double y;
		y = 1.5*x / pow((1+x*x), 2) - 0.65 * atan(1/x) + 0.65*x / (1+x*x);
		return y;
}

double fp(double x)
{
		double y;
		y = (2.8 - 3.2*x*x) / pow((1+x*x), 3);
		return y;
}
double newton_raphson(double x, double eps)
{
		double x1, dx, fx, fpx;

		do {
			fx = f(x);
			fpx = fp(x);
		
			if (fabs(fpx) < EPS0)
			{
				printf( "Warning: slope --> 0 !!!\n");
				break;
			}

			x1 = x - fx/fpx;
			dx = x1 - x;
			x = x1;
		
		} while (fabs(dx) > eps || fabs(fx) > EPS0);

		return x1;
}